A Tikka in 7mm Rem Mag would be hard to beat.
By most accounts, the Tikka is accurate, reliable, light weight, and reasonably priced.
7mm Mag is a good all around cartridge. Particularly if you reload. A 1:9.5 twist barrel on the factory Tikka (and most other factory rifles) will hold you back for the heaviest bullets, but anything between 120 gr and 175 gr will work great. Plenty of horsepower for an elk or bear, but by no means excessive for deer. With heavier bullets, it is also an outstanding long range gun for plinking steel.
I have a load with the 175 ELD-X bullet that pushes 3300 ftlbs, and will stay supersonic to about 2000 yds. I'd not hesitate to shoot an elk at 650 yds with it. For a lighter recoiling deer rifle, you could run a 140-160 gr bullet at moderate speeds, and still outperform the average 30-06 or 308 in drop, wind, and terminal performance.
Also, since it sounds like you're a beginner, loaded factory ammo is everywhere and reasonably priced, and there are tons of good reloading components and load data available.